The Lagrange Multipliers Needed to Find the Maximum and Minimum $f ( x , y ) =$

Essay

The Lagrange multipliers needed to find the maximum and minimum values of $f ( x , y ) =$ 8xy on the circle $x ^ { 2 } + y ^ { 2 } = 25$ is $\lambda = \pm 4$ , where $\nabla f = \lambda \nabla g$ .Estimate the maximum and minimum values of 8xy subject to the constraint $x ^ { 2 } + y ^ { 2 } = 30.25$ .